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Extract the number of supporters for each team from the bar chart.
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Step-by-step solution
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TASK (Bar Chart to Pie Chart)
Extract the number of supporters for each team from the bar chart.
- Team P: 10 supporters
- Team Q: 25 supporters
- Team R: 20 supporters
- Team S: 5 supporters
Calculate the total number of supporters.
Calculate the angle for each team in the pie chart.
The full circle is .
- Team P:
- Team Q:
- Team R:
- Team S:
Calculate the percentage for each team (optional, but good for labeling).
- Team P:
- Team Q:
- Team R:
- Team S:
To represent this data on a pie chart:
- Draw a circle.
- Using a protractor, draw sectors with the calculated angles from the center of the circle.
- Label each sector with the team name and its corresponding percentage or number of supporters.
Item four (Circular Fence)
Identify the given information for the triangular land.
Let the two given sides be m and m.
The angle between them is .
The circular fence touches all three vertices, meaning it is the circumcircle of the triangle.Calculate the length of the third side () using the Law of Cosines.
The Law of Cosines states .
Calculate the diameter of the circular fence (circumcircle) using the Sine Rule.
The Sine Rule states , where is the circumradius and is the diameter.
The diameter of the circular fence is .
Calculate the radius of the circular fence.
Determine the area of the circular fence.
The area of a circle is .
The area of the circular fence is .
To draw an accurate diagram:
- Draw a line segment, representing side m, to scale (e.g., 5.5 cm).
- At one end of this segment, use a protractor to draw an angle of .
- Along the ray of the angle, measure and mark a point representing side m, to the same scale (e.g., 6.4 cm).
- Connect the ends of the two scaled sides to complete the triangle.
- To find the center of the circular fence (circumcenter), construct the perpendicular bisectors of any two sides of the triangle. The point where they intersect is the circumcenter.
- Place the compass point at the circumcenter and extend the pencil to any vertex of the triangle. Draw the circle. This is the circular fence.
- Measure the diameter of this drawn circle (to scale) to verify your calculated diameter.
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